Answer: Two of any three integers must be odd or even, so the sum of these two numbers is even.

2.( 1) Select 52 natural numbers from 1 to 100, and the sum of the two numbers must be 102. Why?

A: Among the natural numbers from 1 to 100, the sum of any two different numbers of 49 groups of a * * is 102.

Namely: 2+ 100, 3+99, ..., 50+52.

In addition to these 49 groups, there is a number of 100-2*49=2.

Because 49+2 = 5 1

Then take 52 numbers, there must be one of the 49 groups, so the sum of the two numbers must be 102.

(2) Take 27 different numbers from all odd numbers from 1 to 100, and the sum of the two numbers must be equal to 102. Please explain the reason.

Answer: As mentioned above, among all odd numbers from 1 to 100, there are 24 groups whose sum of any two odd numbers is 102, namely:

3+99,5+97,....,49+53

In addition to these 24 groups, there are odd numbers of 50-24*2=2.

Because 24+2 = 26

So if we take 27 different odd numbers, there must be one of the 24 groups, so the sum of the two numbers must be equal to 102.